Trans-dimensional geoacoustic inversion

Abstract

This paper develops a general trans-dimensional Bayesian methodology for geoacoustic inversion. Trans-dimensional inverse problems are a generalization of fixed-dimensional inversion that includes the number and type of model parameters as unknowns in the problem. By extending the inversion state space to multiple subspaces of different dimensions, the posterior probability density quantifies the state of knowledge regarding inversion parameters, including effects due to limited knowledge about appropriate parametrization of the environment and error processes. The inversion is implemented here using a reversible-jump Markov chain Monte Carlo algorithm and the seabed is parametrized using a partition model. Unknown data errors are addressed by including a data-error model. Jumps between dimensions are implemented with a birth-death methodology that allows transitions between dimensions by adding or removing interfaces while maintaining detailed balance in the Markov chain. Trans-dimensional inversion results in an inherently parsimonious solution while partition modeling provides a naturally self-regularizing algorithm based on data information content, not on subjective regularization functions. Together, this results in environmental estimates that quantify appropriate seabed structure as supported by the data, allowing sharp discontinuities while approximating smooth transitions where needed. This approach applies generally to geoacoustic inversion and is illustrated here with seabed reflection-coefficient data.

Bayesian evidence computation for model selection in non-linear geoacoustic inference problems

“…32 Model selection can also be addressed by treating the problem as trans-dimensional 33 and applying reversible-jump Markov chains that can jump between parameter spaces of different dimensionality. 12,28,34 Asymptotic point estimates, such as the Bayesian information criterion (BIC), 35,36 are commonly used to carry out model selection. 10,11 The BIC accounts for the number of data and is given by…”

“…However, Bayesian model selection, a fundamental component of Bayesian inference, has seen only limited applications in acoustics. [8][9][10][11][12] Both parameter inference and model selection are intrinsic parts of estimating parameter uncertainty.…”

Varying dimensional Bayesian acoustic waveform inversion for 1D semi-infinite heterogeneous media

“…However, a limited number of studies have addressed the subsurface parameter estimation as a model selection problem, many of which resort to approximate methods to fulfill the model determination [10,13]. The varying dimensional formulation was first introduced to the geophysics literature by Malinverno [31] in a 1D-DC resistivity sounding inversion, and later implemented in a number of geophysical probing inverse problems [39,11,1,35].…”

Seismic inversion and uncertainty analysis using a transdimensional Markov chain Monte Carlo method

“…The rjMCMC was first applied in geophysics in 2000 in an inversion study of zero-offset vertical seismic profiles (Malinverno, 2000;Malinverno and Leaney, 2000). Since then, it has been utilized in a variety of geophysical inverse problems, including earthquake seismology and tomography Agostinetti and Malinverno, 2010;Bodin et al, 2012a,b;Young et al, 2013;Zulfakriza et al, 2014;Kolb and Lekić, 2014;Galetti et al, 2015), geoacoustic inversion (Dettmer et al, 2010;Dettmer and Dosso, 2012;Steininger et al, 2013;Dettmer et al, 2013;Dosso et al, 2014), and electrical and magnetotelluric geophysics (Malinverno, 2002;Minsley, 2011;Brodie and Sambridge, 2012;Ray and Key, 2012;JafarGandomi and Binley, 2013;Ray et al, 2014;Gehrmann et al, 2015). Dadi (2014) and Dadi et al (2015) used rjMCMC for seismic impedance inversion, uncertainty estimation and well log upscaling.…”